1. Recall the model for a simple linear regression: where is Normally distributed with mean 0 and variance , where Cov( ) = 0 for all i, j and Cov( = 0 for all i,j.A day trader wishes to develop a prediction model for a given stock based on the time of day. Each hour the stock market is open for a period of 30 days, the trader collects the following data; Yi = the current stock price and Xi = the time of day. At the end of 30 days the trader runs a simple linear regression on Yi versus Xi and obtains the desired prediction model. What possible mistakes might the day trader have made in conducting this regression analysis?
2. In the simple linear regression model (see above), the are the error terms. That is, the deviations of the actual Yi values from the predicted values using the true regression line. The residuals or values are the deviations of the actual Yi values from estimated regression line. That is. Calculate.
3. Consider the following data: X = Median diameter of granules of sand in (mm)
Y = The gradient of the beach slope in (degrees). Obtain the simple linear regression of Y on X.
|
X =
|
0.170
|
0.190
|
0.220
|
0.235
|
0.235
|
0.300
|
0.350
|
0.420
|
0.850
|
|
Y =
|
0.630
|
0.700
|
0.820
|
0.880
|
1.150
|
1.500
|
4.400
|
7.300
|
11.300
|
a. Find a 95% confidence interval for
b. Find a 95% confidence interval for β
4. Using the simple linear regression equation of problem 3. Find use this to prepare a 95 % confidence interval for E[
5. Use the results of the simple regression obtained in problem 3 to compute:
a. The sample covariance between (X and Y)
b. The sample correlation coefficient between X and Y